Federation is kinda sorta like email. It's not all centralized on one universal server, but many! Thousands! There's no one universal all-controlling "center."
I was wondering, what EXACTLY I see in the "public stream".
That depends on what your site administrator wants you to see there. Some only allow public posts that originate on this site. Some allow you to see any public posts in the network. This will include all public posts on this site, all incoming public posts from other networks/protocols, and a random sampling of public posts from elsewhere in the Hubzilla universe. A number of sites turn this off completely as the content is unmoderated and could be illegal in some jurisdictions.
I see, thank you! As I am the admin and the only user, I am the only one who will ever see my public stream, right? So, I don’t have to bother about illegal content.
Not necessarily. You might want to tick the box to only allow authenticated viewers, or else this will be open to the public. See admin/site. There are a few public stream settings. Authenticated viewers also includes remote auth viewers from other hubzilla sites. You may want a setting to restrict this to only local logins but nobody has done this yet.